The personality of King Lear is based on the fact that he is a King. He enjoys the powers and responsibilities as well as getting to rule over others. As shown by his response to Kent, Lear does not do well to people contradicting his rulings.
Walter White is a power hungry man who, like Lear, fears of losing family, money, and power and decides to start making meth. He becomes fixated on gaining power and being the best which harms his home life. Like Lear, White does not do well when people contradict him and this tends to happen often. His reaction is matched to Lear’s, White wants them out of the picture if they don’t agree.
Once both Lear and White start to lose power they will do anything to get it back. Because of their position of power they also have people trying to take them down or take some of their power. For Lear this is his own daughters Goneril and Regan and for White (without trying to spoil much) this is the people he works for. Lear realizes the loyalty of his youngest daughter Cordelia, but was he too late to see this like White was? Without spoiling the end of Breaking Bad, I will say that it also ends in a tragedy. Throughout the season many people find themselves backstabbing people you thought they trusted and going against each other.